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nika2105 [10]
3 years ago
5

Please Help!!! 30 Points!!

Mathematics
1 answer:
LenaWriter [7]3 years ago
4 0

Answer:

  8.170

Step-by-step explanation:

\log_2{288}=\log_2{2^53^2}=\log_2{2^5}+\log_2{3^2}\\\\=5\log_2{2}+2\log_2{3}\approx 5+2(1.5850)=8.170

_____

Your calculator can help you check this result.

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<h3>Answer: Choice D. </h3>

Morgan forgot to distribute the negative sign to two of the terms in the second expression.

=============================================================

Explanation:

Focus on the numerators.

We have (3t^2-4t+1) as the first numerator and we subtract off (t^2+2t+2) as the second numerator.

Morgan needs to simplify (3t^2-4t+1)-(t^2+2t+2) for the numerator.

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(3t^2-4t+1)-(t^2+2t+2)

3t^2-4t+1-t^2+2t+2 .... her mistake made here

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Here's what Morgan should have for her steps when simplifying the numerator.

(3t^2-4t+1)-(t^2+2t+2)

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Note in the second step, the negative outside flips the sign of each term in the second parenthesis.

Therefore,

\frac{3t^2-4t+1}{t+3}-\frac{t^2+2t+2}{t+3}\\\\\frac{(3t^2-4t+1)-(t^2+2t+2)}{t+3}\\\\\frac{3t^2-4t+1-t^2-2t-2}{t+3}\\\\\frac{2t^2-6t-1}{t+3}\\\\

which means \frac{3t^2-4t+1}{t+3}-\frac{t^2+2t+2}{t+3}=\frac{2t^2-6t-1}{t+3}, \ \ \text{ where } t \ne -3\\\\

Side notes:

  • The fractions can only be subtracted since the denominators are the same.
  • We have t \ne -3 to avoid a division by zero error.
  • Rational expressions are a fraction, or ratio, of two polynomials.
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